Algebra : an approach via module theory / William A. Adkins, Steven H. Weintraub.
Series Graduate texts in mathematics ; 136Editor: New York : Springer-Verlag, c1992Descripción: x, 526 p. ; 25 cmISBN: 0387978399; 3540978399 (Berlin)Tema(s): Algebra | Modules (Algebra)Otra clasificación: 00A05 (13-01 15-01 16-01 20-01)Preface v Chapter 1 Groups [1] 1.1 Definitions and Examples [1] 1.2 Subgroups and Cosets [6] 1.3 Normal Subgroups, Isomorphism Theorems, and Automorphism Groups [15] 1.4 Permutation Representations and the Sylow Theorems [22] 1.5 The Symmetric Group and Symmetry Groups [28] 1.6 Direct and Semidirect Products [34] 1.7 Groups of Low Order [39] 1.8 Exercises [45] Chapter 2 Rings [49] 2.1 Definitions and Examples [49] 2.2 Ideals, Quotient Rings, and Isomorphism Theorems [58] 2.3 Quotient Fields and Localization [68] 2.4 Polynomial Rings [72] 2.5 Principal Ideal Domains and Euclidean Domains [79] 2.6 Unique Factorization Domains [92] 2.7 Exercises [98] Chapter 3 Modules and Vector Spaces [107] 3.1 Definitions and Examples [107] 3.2 Submodules and Quotient Modules [112] 3.3 Direct Sums, Exact Sequences, and Hom [118] 3.4 Free Modules [128] 3.5 Projective Modules [136] 3.6 Free Modules over a PID [142] 3.7 Finitely Generated Modules over PIDs [156] 3.8 Complemented Submodules [171] 3.9 Exercises [174] Chapter 4 Linear Algebra [182] 4.1 Matrix Algebra [182] 4.2 Determinants and Linear Equations [194] 4.3 Matrix Representation of Homomorphisms [214] 4.4 Canonical Form Theory [231] 4.5 Computational Examples [257] 4.6 Inner Product Spaces and Normal Linear Transformations [269] 4.7 Exercises [278] Chapter 5 Matrices over PIDs [289] 5.1 Equivalence and Similarity [289] 5.2 Hermite Normal Form [296] 5.3 Smith Normal Form [307] 5.4 Computational Examples [319] 5.5 A Rank Criterion for Similarity [328] 5.6 Exercises [337] Chapter 6 Bilinear and Quadratic Forms [341] 6.1 Duality [341] 6.2 Bilinear and Sesquilinear Forms [350] 6.3 Quadratic Forms [376] 6.4 Exercises [391] Chapter 7 Topics in Module Theory [395] 7.1 Simple and Semisimple Rings and Modules [395] 7.2 Multilinear Algebra [412] 7.3 Exercises [434] Chapter 8 Group Representations [438] 8.1 Examples and General Results [438] 8.2 Representations of Abelian Groups [451] 8.3 Decomposition of the Regular Representation [453] 8.4 Characters [462] 8.5 Induced Representations [479] 8.6 Permutation Representations [496] 8.7 Concluding Remarks 8.8 Exercises [505] Appendix [507] Bibliography [510] Index of Notation [511] Index of Terminology [517]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | 00A05 Ad236 (Browse shelf) | Available | A-6845 |
Incluye referencias bibliográficas (p. [510]) e índices.
Preface v --
Chapter 1 Groups [1] --
1.1 Definitions and Examples [1] --
1.2 Subgroups and Cosets [6] --
1.3 Normal Subgroups, Isomorphism Theorems, and Automorphism Groups [15] --
1.4 Permutation Representations and the Sylow Theorems [22] --
1.5 The Symmetric Group and Symmetry Groups [28] --
1.6 Direct and Semidirect Products [34] --
1.7 Groups of Low Order [39] --
1.8 Exercises [45] --
Chapter 2 Rings [49] --
2.1 Definitions and Examples [49] --
2.2 Ideals, Quotient Rings, and Isomorphism Theorems [58] --
2.3 Quotient Fields and Localization [68] --
2.4 Polynomial Rings [72] --
2.5 Principal Ideal Domains and Euclidean Domains [79] --
2.6 Unique Factorization Domains [92] --
2.7 Exercises [98] --
Chapter 3 Modules and Vector Spaces [107] --
3.1 Definitions and Examples [107] --
3.2 Submodules and Quotient Modules [112] --
3.3 Direct Sums, Exact Sequences, and Hom [118] --
3.4 Free Modules [128] --
3.5 Projective Modules [136] --
3.6 Free Modules over a PID [142] --
3.7 Finitely Generated Modules over PIDs [156] --
3.8 Complemented Submodules [171] --
3.9 Exercises [174] --
Chapter 4 Linear Algebra [182] --
4.1 Matrix Algebra [182] --
4.2 Determinants and Linear Equations [194] --
4.3 Matrix Representation of Homomorphisms [214] --
4.4 Canonical Form Theory [231] --
4.5 Computational Examples [257] --
4.6 Inner Product Spaces and Normal Linear Transformations [269] --
4.7 Exercises [278] --
Chapter 5 Matrices over PIDs [289] --
5.1 Equivalence and Similarity [289] --
5.2 Hermite Normal Form [296] --
5.3 Smith Normal Form [307] --
5.4 Computational Examples [319] --
5.5 A Rank Criterion for Similarity [328] --
5.6 Exercises [337] --
Chapter 6 Bilinear and Quadratic Forms [341] --
6.1 Duality [341] --
6.2 Bilinear and Sesquilinear Forms [350] --
6.3 Quadratic Forms [376] --
6.4 Exercises [391] --
Chapter 7 Topics in Module Theory [395] --
7.1 Simple and Semisimple Rings and Modules [395] --
7.2 Multilinear Algebra [412] --
7.3 Exercises [434] --
Chapter 8 Group Representations [438] --
8.1 Examples and General Results [438] --
8.2 Representations of Abelian Groups [451] --
8.3 Decomposition of the Regular Representation [453] --
8.4 Characters [462] --
8.5 Induced Representations [479] --
8.6 Permutation Representations [496] --
8.7 Concluding Remarks --
8.8 Exercises [505] --
Appendix [507] --
Bibliography [510] --
Index of Notation [511] --
Index of Terminology [517] --
MR, 94a:00001
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